Problem 9-17 Constant growth Your broker offers to sell you some shares of Bahns
ID: 2650041 • Letter: P
Question
Problem 9-17
Constant growth
Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $3.00 yesterday. Bahnsen's dividend is expected to grow at 7% per year for the next 3 years. If you buy the stock, you plan to hold it for 3 years and then sell it. The appropriate discount rate is 11%.
Find the expected dividend for each of the next 3 years; that is, calculate D1, D2 and D3. Note that D0 = $3.00. Round your answer to the nearest cent.
D1 = $
D2 = $
D3 = $
Given that the first dividend payment will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PVs of D1, D2, and D3 and then sum these PVs. Round your answer to the nearest cent.
$
You expect the price of the stock 3 years from now to be $98.31; that is, you expect P3 to equal $98.31. Discounted at a 11% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $98.31. Round your answer to the nearest cent.
$
If you plan to buy the stock, hold it for 3 years, and then sell it for $98.31, what is the most you should pay for it today? Round your answer to the nearest cent.
$
calculate the present value of this stock?
??????
Assume that g = 7% and that it is constant. Round your answer to the nearest cent.
$
Explanation / Answer
1. D1 = 3 x 1.071 = $3.21
D2 = 3 x 1.072 = $3.43
D3 = 3 x 1.073 = $3.68
2. Present value of D1 = 3.21 / (1 + 0.11)1 = $2.89
Present value of D2 = 3.43 / (1 + 0.11)2 = $2.78
Present value of D3 = 3.68 / (1 + 0.11)3 = $2.69
Total = 2.89 + 2.78 + 2.69 = $8.36
3. Present value of this expected future stock price = 98.31 / (1 + 0.11)3 = $71.88
4. The most we should pay = present value of all dividend and stock price after 3 years = 8.36 + 71.88 = $80.24
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